Question: Solve for $x$ : $5x^2 - 15x - 270 = 0$
Explanation: Dividing both sides by $5$ gives: $ x^2 {-3}x {-54} = 0 $ The coefficient on the $x$ term is $-3$ and the constant term is $-54$ , so we need to find two numbers that add up to $-3$ and multiply to $-54$ The two numbers $6$ and $-9$ satisfy both conditions: $ {6} + {-9} = {-3} $ $ {6} \times {-9} = {-54} $ $(x + {6}) (x {-9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 6) (x -9) = 0$ $x + 6 = 0$ or $x - 9 = 0$ Thus, $x = -6$ and $x = 9$ are the solutions.